If you want to experience a real Tel-Aviv/Israeli bar you must check out the Tepale’. It is in the center of town (King George / Shlomo hamelech) and is supper cheep. They play great music and have a chilled atmosphere. It is NOT a kids bar so dont expect drunk college girls jumping around.
If you want the hard core experience go to the friday “kabalat shabat” at 2pm.
By the way, they are closed on Friday night 🙂